Ukraine's interim president Oleksander Turchinov earlier insisted the offensive was going ahead but then sacked the state security chief in charge of the operation.
Turchinov also took a risky step to try to undercut rebels' demands, by holding out the prospect of a referendum on the future shape of the Ukrainian state.
He suggested this could be held at the same time as a presidential election on May 25.
The initiative came as the European Union threatened Russia with more sanctions over its actions in eastern Ukraine, which Britain said was being destabilised by Moscow, although some EU states said diplomacy should be given more time.
As the deadline issued by authorities in Kiev expired, in Slaviansk, which was expected to be the focus of a government "anti-terrorist" operation involving the army, there was no sign that armed men, who had seized two govern-ment buildings, were obeying the ultimatum. In contrast, one rebel leader, in an appeal issued through journalists, asked Russian President Vladimir Putin to "help us as much as you can".
A group of about 12 armed men in matching camouflage fatigues, with black balaclavas, stood outside the city council offices, one holding a Russian flag.
They said they were Cossacks but did not say where from. One said: "The borders between Ukraine, Russia and Belarus are artificial and we are here to take them away."
Also in Slaviansk, about 90 miles from the Russian border, an airfield occupied by Ukrainian air force planes on Sunday was empty yesterday and pro-separatist forces said they were now in control of it.
Meanwhile, in the city of Horlivka about 100 pro-Russian separatists attacked the police headquarters, a witness said.
Video footage on Ukrainian television showed an ambulance crew treating people apparently injured in the attack.
In all, separatists have seized government buildings and security facilities in 10 cities.
Earlier, angered by the death of a state security officer and the wounding of two comrades near Slaviansk, Turchinov had warned rebels that an anti-terrorist operation involving the army would begin unless they laid down their arms, and that the Donbass region of eastern Ukraine "will soon be stabilised".
The warning raised fears of possible Russian military intervention like that in Crimea which Moscow finally annexed from Ukraine last month.
The new element in the operation announced by Turchinov was the inclusion of the army, which has not been involved in more than four months of turmoil and is untested in dealing with internal disorder.
The plan to bring in the army shows a lack of confidence in the 30,000-strong interior ministry troops discredited by identification with the leadership of ousted president Viktor Yanukovich.
The defence ministry yesterday would not comment on the army's role.